If the discriminant of a quadratic equation has the given value, determine the number and type of solutions of the equation.
A.48
B.0
If b^2-4ac = +48 then you have two real roots
If b^2 -4ac = 0 then your two roots are the same and you really only have one real root. The vertex is on the x axis.
To determine the number and type of solutions of a quadratic equation using the discriminant, we need to calculate the discriminant first. The discriminant is the expression under the square root in the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the discriminant has a value of 48. The discriminant is calculated using the formula:
Discriminant (D) = b^2 - 4ac
A. For a discriminant value of 48 or any positive number, we have two real and distinct solutions. This means that the quadratic equation has two different real roots.
B. For a discriminant value of 0, there is one real solution. This means that the quadratic equation has one repeated real root.
By plugging the value of the discriminant into the formula, we can solve for the number and type of solutions for the quadratic equation.